<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1">
<title>Tutorial: H+ affinity diagram</title>
<style type="text/css"> <!-- @import url(1_.css);   --> </style>
<link disabled rel="stylesheet" type="text/css" href="1_.css">
</head>

<body bgcolor="#ffffff" text="#000000" link="#008000" vlink="#008000" alink="#008000">
<table cellspacing="0" cellpadding="0" border="0">
  <tr>
    <td align="center" valign="middle" width="50">
    <a href="0_Index.htm"><img src="images/thco35_s.gif" border="0" width="32" height="32" alt="Chem.Eq.Diagr"></a>&nbsp;</td>
    <td align="left" valign="middle"><font size="-1"><a href="0_Index.htm">Chemical Equilibrium Diagrams</a>&nbsp;/ <a href="Tut_0_Tutorials.htm">Tutorials</a></font></td>
  </tr>
</table>

<h3>Proton affinity diagrams</h3>

<p>This diagram type can only be selected in SPANA with the
&#147;advanced&#148; program level (in the menu Preferences / General options).</p>

<p>A proton affinity curve made with Spana will show the derivative of bound
<nobr>H<sup>+</sup></nobr> ions with respect to the logarithm of the
<nobr>H<sup>+</sup></nobr> activity:
<table cellspacing="0" cellpadding="0" border="0">
 <tr valign="center"><td><tt>&nbsp;&nbsp;</tt></td>
 <td>
    <table cellspacing="0" cellpadding="0" border="0">
    <tr valign="baseline">
    <td><nobr><i>d</i> [H<sup>+</sup>]<sub>bound</sub></nobr></td><td></td>
    </tr>
    <tr valign="baseline"><td><hr></td></tr>
    <tr valign="baseline">
    <td align="center"><nobr><i>d</i> (log <i>a</i><sub><span>H<sup>+</sup></span></sub>)</nobr></td><td></td>
    </tr>
    </table>
  </td>
  </tr>
</table>
this can be plotted against pH, for example. Remember that
<nobr>log <i>a</i><sub>H<font size="+1"><sup>+</sup></font></sub></nobr> = <nobr>&#8722;pH.</nobr>
The amount of bound <nobr>H<sup>+</sup></nobr> is calculated as:
<table cellspacing="0" cellpadding="0" border="0">
 <tr valign="baseline"><td><tt>&nbsp;&nbsp;</tt></td>
 <td><nobr>[H<sup>+</sup>]<sub>bound</sub></nobr></td>
  <td><tt>&nbsp;=&nbsp;</tt></td>
  <td> <nobr>[H<sup>+</sup>]<sub>TOT</sub></nobr>
    <nobr>&#8722; [H<sup>+</sup>]</nobr> <nobr>&#8722; [OH<sup>&#8722;</sup>]</nobr></td>
  </tr>
</table></p>
<p>This is the amount of <nobr>H<sup>+</sup></nobr> bound in different species,
for example in <nobr>HCO<sub>3</sub><sup>&#8722;</sup></nobr> or in
<nobr>Al(OH)<sub>4</sub><sup>&#8722;</sup>.</nobr>
The derivative is approximated numerically:</p>
<table cellspacing="0" cellpadding="0" border="0">
 <tr><td><tt>&nbsp;&nbsp;</tt></td>
 <td valign="top">
    <table cellspacing="0" cellpadding="0" border="0">
    <tr valign="baseline">
    <td><nobr><i>d</i> [H<sup>+</sup>]<sub>bound</sub></nobr></td><td></td>
    </tr>
    <tr valign="baseline"><td><hr></td></tr>
    <tr valign="baseline">
    <td align="center"><nobr><i>d</i> (log <i>a</i><sub><span>H<sup>+</sup></span></sub>)</nobr></td><td></td>
    </tr>
    </table>
  </td>
  <td  valign="middle"><table cellspacing="0" cellpadding="0" border="0">
  <tr><td>&nbsp;</td></tr><tr><td>
  <tt>&nbsp;=&nbsp;</tt></td></tr><tr><td>&nbsp;</td></tr></table>
  </td>
 <td valign="top">
    <table cellspacing="0" cellpadding="0" border="0">
    <tr valign="baseline">
    <td><nobr>&#916; [H<sup>+</sup>]<sub>bound</sub></nobr></td>
    </tr>
    <tr valign="baseline"><td><hr></td></tr>
    <tr valign="baseline">
    <td><nobr>&#916; (&#8722;pH)</nobr></td>
    </tr>
    </table>
  </td>
  </tr>
</table>
If a value for the <a href="SP_Ionic_Strength.htm">ionic strenght</a>
is <b>not</b> <a href="S_Making_Diagrams.htm#Parameters">given in Spana</a> when
making the diagram, then pH = <nobr>&#8722;log [H<sup>+</sup>].</nobr></p>

<p>The resulting diagram shows a peak for each protonation reaction,
and it can be more useful than the corresponding titration curve. Unfortunately
peaks may overlap, and a diagram&rsquo;s interpretation is never unique.</p>

<h4><a name="Top"></a>Examples:</h4>
<ul style="margin-top:10pt">
  <li><b><a href="#Citric">Citric acid</a></b></li>
  <li><b><a href="#Mix">Mixture of oxalate and carbonate</i></a></b></li>
  <li><b><a href="#Al_Hydrolysis">Al(III) hydrolysis</i></a></b></li>
  </ul>
<a name="Citric"></a>
<hr><!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -->


<h3>Citric acid</h3>

<p>Select citrate <nobr>(cit<sup>3&#8722;</sup>)</nobr> and <nobr>H<sup>+</sup></nobr>
as components in DATABASE. In SPANA make sure you have selected the
&#147;advanced&#148; program level (in the menu Preferences / General options).</p>

<p>Make and compare the titration curves <b>without</b> and <b>with</b> citrate:
<center>
<img src="images/H_aff_citr_1.gif" alt="Titration_citr = 0" title="Titration_citr = 0" height="223" width="300" border="1">
</center>
<center>
<img src="images/H_aff_citr_2.gif" alt="Titration_citr" title="Titration_citrate" height="223" width="300" border="1">
</center>
</p>
<p>It is difficult to tell what kind of ligand is present only by looking at these
curves. By taking the derivative, making a proton affinity diagram,
it becomes clear that there are three protonation sites:
<center>
<img src="images/H_aff_citr_3.gif" alt="Titration_citr_H-affinity" title="Titration_citr_H-affinity" height="223" width="300" border="1">
</center>
</p>

<a name="Mix"></a>
<table width="100%" cellspacing="0" cellpadding="0" border="0">
<tr><td><hr><!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -->
</td><td width="20" align="right">
<a href="#Top"><img src="images/Upp.gif" alt="top" title="top" height="15" width="15" border="0"></a>
</td></tr></table>

<h3>Mixture</h3>

<p>Select oxalate <nobr>(ox<sup>2&#8722;</sup>),</nobr> carbonate
<nobr>(CO<sub>3</sub><sup>2&#8722;</sup>)</nobr> and <nobr>H<sup>+</sup></nobr>
as components in DATABASE. In SPANA make sure you have selected the
&#147;advanced&#148; program level (in the menu Preferences / General options).</p>

<p>When a mixture of ligands is presents (in this case <nobr>ox<sup>2&#8722;</sup></nobr> and
<nobr>CO<sub>3</sub><sup>2&#8722;</sup>)</nobr> in the proton affinity diagram
the height of the peaks is proportional to the concentration of the corresponding
ligand. For example:</p>
<p><center>
<img src="images/H_aff_mix.gif" alt="Proton_affinity_diagram_Mixture" title="Proton_affinity_diagram_Mixture" height="223" width="300" border="1">
</center>
Note that the peaks are located at the pH corresponding to the acid constant.</p>

<a name="Al_Hydrolysis"></a>
<table width="100%" cellspacing="0" cellpadding="0" border="0">
<tr><td><hr><!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -->
</td><td width="20" align="right">
<a href="#Top"><img src="images/Upp.gif" alt="top" title="top" height="15" width="15" border="0"></a>
</td></tr></table>

<h3>Al(III) hydrolysis</h3>

<p>An example where several peaks are overlapping in a proton affinity diagram.</p>

<p>Select <nobr>Al<sup>3+</sup></nobr> and <nobr>H<sup>+</sup></nobr>
as components in DATABASE. In SPANA make sure you have selected the
&#147;advanced&#148; program level (in the menu Preferences / General options).</p>

<p>Select the menu &#147;Run&nbsp;/
<a href="S_Modify_Chem_System.htm">Modify chemical <nobr>system</a>&#148;.</nobr>
Double click on each of the crystalline phases (both <nobr>Al(OH)<sub>3</sub>(cr)</nobr> and
<nobr>AlOOH(cr))</nobr> and <a href="S_Modify_Chem_System.htm#Mod_logK">deactive</a> them.
Save the file. With this change only the more soluble amorphous hydroxide can
precipitate.</p>

<p>Make a proton affinity diagram for <nobr>[Al(III)]<sub>TOT</sub></nobr> =
<nobr>10<sup>&#8722;6</sup>M.</nobr> With this low concentration the Al-hydroxide
does not precipitate. The diagram shows two peaks:</p> 
<p><center>
<img src="images/H_aff_Al_0.gif" alt="Proton_affinity_diagram_Al" title="Proton_affinity_diagram_Al" height="221" width="300" border="1">
</center>
However, the corresponding logarithmic diagram:</p>
<p><center>
<img src="images/H_aff_Al_1.gif" alt="Log_diagram_Al" title="Log_diagram_Al" height="221" width="300" border="1">
</center>
shows that several protonation reactions are included in each peak.</p>


<p style="text-align:right; line-height:0; margin-top:0; margin-bottom:0">
<a href="#Top"><img src="images/Upp.gif" alt="top" title="top" height="15" width="15" border="0"></a>
</p>
</body>
</html>